Definition 2.14 (cf. [1]}) 
 Suppose \(f : X \rightarrow \overline{\mathbf {R}}\)  is convex and \(x\in X\)  is such that \(f(x) \in \mathbf {R}\) . We say that \( \zeta \in X \)  is a
subgradient of \(f\)  at \(x\) if
\(f^{\prime }(x;v) \ge \zeta \bullet v \quad \text{for $ v \in X $.}\) 
